6 citations · 8 across the 8 of their papers we have counts for
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Diophantine approximation and badly approximable sets
Simon Kristensen, Rebecca Thorn, Sanju Velani
Let (X,d) be a metric space and (Ω, d) a compact subspace of X which supports a non-atomic finite measure m. We consider `natural' classes of badly approximable subsets of Ω. Loose…
Metric Diophantine approximation with respect to planar distance functions
Simon Kristensen
We outline a proof of an analogue of Khintchine's Theorem in R^2, where the ordinary height is replaced by a distance function satisfying an irrationality condition as well as cert…
A quantitative Khintchine-Groshev type theorem over a field of formal series
M. M. Dodson, S. Kristensen, J. Levesley
An asymptotic formula which holds almost everywhere is obtained for the number of solutions to the Diophantine inequalities |qA-p|<ψ(|q|), where A is an n by m matrix (m>1) over th…
A metric theorem for restricted Diophantine approximation in positive characteristic
Simon Kristensen
We calculate the measure and Hausdorff dimension of sets of matrices over fields of formal power series with good approximation properties for a restricted set of denominators.
Zero-infinity laws in Diophantine approximation
Y. Bugeaud, M. M. Dodson, S. Kristensen
It is shown that for any translation invariant outer measure M, the M-measure of the intersection of any subset of R^n that is invariant under rational translations and which does…
Hausdorff Dimension and Diophantine Approximation
M. Maurice Dodson, Simon Kristensen
We begin with a brief treatment of Hausdorff measure and Hausdorff dimension. We then explain some of the principal results in Diophantine approximation and the Hausdorff dimension…